14¢ THEORY OF STATISTICS. 
venience, be taken as origin. Thus in Example ii. the median is 
(Chap. VIL § 15) 3-195 per cent. Hence 3:0 per cent. should be 
taken as the origin, d = + 0-39 intervals, NV; = 327, /,= 305. The 
deviation-sum with 3'0 as origin is found to be 1263, and the 
correction is +039 x 22= +86. Hence the mean deviation 
from the median is 2:012 intervals, or again 1:01 per cent. The 
value is really smaller than that of the mean deviation from the 
arithmetic mean, but the difference is too slight to affect the 
second place of decimals. 
It should be noted that, as in the case of the standard deviation, 
this method of calculation implies the assumption that all the 
values of X within any one class-interval may be treated as if 
they were the mid-value of that interval. This is, of course, an 
approximation; but as a rule gives results of amply sufficient 
accuracy for practice if the class-interval be kept reasonably small 
(¢f. again Chap. VI. § 5). We have left it as an exercise to the 
student to find the correction to be applied if the values in each 
interval are treated as if they were evenly distributed over the 
interval, instead of concentrated at its centre (Question 7). 
18. The mean deviation, it will be seen, can be calculated rather 
more rapidly than the standard deviation, though in the case of a 
grouped distribution the difference in ease of calculation is not 
great. It is not, on the other hand, a convenient magnitude for 
algebraical treatment ; for example, the mean deviation of a dis- 
tribution obtained by combining several others cannot in general 
be expressed in terms of the mean deviations of the component 
distributions, but depends upon their forms. As a rule, it is more 
affected by fluctuations of sampling than is the standard deviation, 
but may be less affected if large and erratic deviations lying 
somewhat beyond the bulk of the distribution are liable to occur. 
This may happen, for example, in some forms of experimental 
work, and in such cases the use of the mean deviation may be 
slightly preferable to that of the standard deviation. 
19. It is a useful empirical rule for the student to remember 
that for symmetrical or only moderately asymmetrical distri- 
butions, approaching the ideal forms of figs. 5 and 9, the mean 
deviation is usually very nearly four-fifths of the standard devia 
tion. Thus for the distribution of pauperism we have 
mean deviation 1-01 0-81 
standard deviation 1:24 ~~ °° 
In the case of the distribution of male statures in the British 
Isles, Example iii., the ratio found is 0:80. For a short series of 
observations like the wage statistics of Example i. a regular result 
could hardly be expected: the actual ratio is 15°0/20'5=0-73. 
0